-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1843044610699859971302967198590', 'a10': [0.3596249068005759, 0.6228886102458198], 'a2': [-1.200270112485709, 0.6929762725438864], 'a3': [1.4128870151086237, 2.447192095522472], 'a4': [-0.03956777138236247, 0.06853339037652163], 'a5': [0.0, -0.5189570278941993], 'a6': [-3.3916921131080504, -1.9581943545112634], 'a7': [-0.8660254037844386, -0.5], 'a8': [0.0, -2.8815831970772185], 'a9': [-2.492499434925112, 4.31713565912701], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-1.426413659428095, -3.311396091106733]]]], 'bad_primes': [7, 13], 'central_character': '91.36', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '4349881023299013006950880886125', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.200270112485709, -0.6929762725438864], [1.0, -1.7320508075688772]], [[1.0, 0], [-1.4128870151086237, -2.447192095522472], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0.5189570278941993], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-1.406563288575936, 0.8120796932915619], [5.5, -9.526279441628825]], [[1.0, 0], [-1.426413659428095, -3.311396091106733]], [[1.0, 0], [-0.9741265655433228, 1.687236704523609], [-8.5, -14.722431864335457]], [[1.0, 0], [-2.157403431432799, -1.2455774518883487], [9.5, 16.454482671904334]], [[1.0, 0], [4.5702904465414225, 7.915975258756395], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.6149785357945103, -4.529275684698161], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 5.793909608153129], [-31.0, 0]], [[1.0, 0], [8.858794990628247, -5.114627672534928], [18.5, -32.04293994002423]], [[1.0, 0], [-3.6451281885049585, 2.1045157408640307], [20.5, -35.50704155516198]], [[1.0, 0], [0.4986554688515856, -0.863696607523026], [-21.5, -37.239092362730865]], [[1.0, 0], [0, 4.517254438312114], [-47.0, 0]], [[1.0, 0], [8.896506262173292, 0], [53.0, 0]], [[1.0, 0], [5.373915820654569, 3.1026317456573045], [29.5, 51.09549882328188]], [[1.0, 0], [-6.735362135655323, 11.66598942633064], [-30.5, -52.827549630850754]], [[1.0, 0], [7.250936288253711, -4.186330017900106], [33.5, -58.023702053557386]], [[1.0, 0], [4.501680285713726, 2.5990463247624507], [35.5, 61.48780366869514]], [[1.0, 0], [0, 11.8395287782885], [-73.0, 0]], [[1.0, 0], [-0.982309807553395, 0], [79.0, 0]], [[1.0, 0], [0, -8.918510780150873], [-83.0, 0]], [[1.0, 0], [10.408746652108302, -6.009492681521345], [44.5, -77.07626093681505]], [[1.0, 0], [-3.829811008655439, -2.21114241679261], [48.5, 84.00446416709055]], [[1.0, 0], [-9.15132497599582, -15.850559814998798], [-50.5, 87.4685657822283]], [[1.0, 0], [5.020455469297848, 0], [103.0, 0]], [[1.0, 0], [3.0722795473478137, 5.321344271061126], [-53.5, 92.66471820493493]], [[1.0, 0], [0, 11.89624635280951], [-109.0, 0]], [[1.0, 0], [1.7780611241020194, -3.0796922059077287], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-91-13.10-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/36/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7794450660381287, 0.7243830138884935, 0.6774990182741161, 0.635081045318776, 0.5932861459035946, 0.5484306316538172, 0.4972123366581962, 0.4368702398674035, 0.36530780553599257, 0.2812060397717841, 0.18414121068121672, 0.07470982887598628, -0.045346068626773074, -0.17302649771809422, -0.30399069086502317, -0.4325221730551607, -0.5515601204966055, -0.6528139486969389, -0.7269751305360389, -0.7640356892832734, -0.7537166170505812, -0.6860017272446777, -0.5517634123392168, -0.3434568805862708, -0.05584930831272535, 0.313259240230553, 0.7623743810139608, 1.2857623529592197, 1.873080382189224, 2.509239312006172, 3.1745480944725126, 3.8451770833614707, 4.493959064716962, 5.091524174438301, 5.607738397360589, 6.013386886571639, 6.282015049769664, 6.3918147664376015, 6.3274229724507265, 6.081487892207131, 5.655856819775713, 5.0622503548285, 4.322312302375406, 3.4669618294904434, 2.535023415209944, 1.571167743493428, 0.6232587917098843, -0.2607362946734439, -1.0360633270118418, -1.664470211799047, -2.1171929055343597, -2.377361958829005, -2.4415794509814925, -2.3204687854985364, -2.0380770239236603, -1.630106245151148, -1.1410592119495104, -0.6204955752507024, -0.11869669554333455, 0.31788170820512524, 0.6509401910094915, 0.8540109064991024, 0.9150744137173186, 0.837795870988137, 0.6411809854806206, 0.357606375817939, 0.029350964102811204, -0.29607302058577983, -0.5713383645346491, -0.754905673775237, -0.8161873492523476, -0.7396580025313672, -0.5273771225646515, -0.19953906941847344, 0.20712837990041832, 0.6430525545244374, 1.0512732195190788, 1.374115876381681, 1.5603433389862478, 1.5719397093899792, 1.3896691335085964, 1.016645731342368, 0.4793475588454654, -0.1742103478773017, -0.8790900756034129, -1.560422099533237, -2.1420346430994206, -2.555724934302638, -2.7500300616919398, -2.69734765583563, -2.3983991510936, -1.883313141450658, -1.2090057961162695, -0.4530042153877909, 0.2956612335117503, 0.9474424295265663, 1.4237715139070497, 1.6675596229158751, 1.651235467961021, 1.3811176591637369, 0.897351722213653, 0.2692133382625312, -0.41378770545276256, -1.0539581238243536, -1.5590819355320296, -1.8558363057282947, -1.9010418880539768, -1.6890321798029813, -1.2538895002170007, -0.6659656004888187, -0.022898267529552225, 0.5638562921010908, 0.9852490984231678, 1.1514010491774036, 1.0064834575061754, 0.5394424621653835, -0.21122016135889152, -1.1596220849767014, -2.1816789941045265, -3.1303132304303873, -3.8547910611635148, -4.221595436257258, -4.133901078348801, -3.546798331034404, -2.475918815721458, -0.9979921585156878, 0.7570080215528078, 2.6212501503447454, 4.409954340630568, 5.944954397857491, 7.077586722298752, 7.707618329945764, 7.795464945349136, 7.365920195617531, 6.502877786936017, 5.335888606858079, 4.020640545068336, 2.7163792271488574, 1.5637472708521347, 0.6664255860374013, 0.0793193890939077, -0.195058153331426, -0.20171494650127245, -0.020942868856650226, 0.24894463098935482, 0.5107426679389107, 0.6859277581543648, 0.727583900997805, 0.6264795842647317, 0.40938121401968197, 0.1301503237907544, -0.14445639208158711, -0.35133883186431886, -0.44652995475434426, -0.41633767248196785, -0.28169741431096745, -0.09458935785112262, 0.07304544159975097, 0.14589766134730056, 0.06416475368831509, -0.1991736640178477, -0.6264841626739159, -1.1519810011880358, -1.668099551809966, -2.0413827310241586, -2.1356130603789385, -1.8383281889567493, -1.0859012638965233, 0.11772951330920275, 1.692765661752758, 3.488112561584128, 5.299008391596325, 6.895528432425953, 8.057644827408497, 8.611068685348778, 8.457632012927863, 7.594618249015069, 6.119155186351303, 4.216275064057203, 2.1320965154005105, 0.13627920834394905, -1.5200603661062215, -2.643805320541778, -3.1297984107812695, -2.9759957507047226, -2.2810700278750575, -1.2248404161997943, -0.03501353647194171, 1.0537700332476285, 1.8411602431671892, 2.1951112771357297, 2.072548301979676, 1.5230644806939426, 0.6752402217301279, -0.291518477054611, -1.1839701984165436, -1.833540649628217, -2.1287854657251812, -2.0355114605224265, -1.6007548314467202, -0.9400756824943628, -0.21100061629444722, 0.421751252638461, 0.8219626978891305, 0.9110676114835953, 0.6846590955661104, 0.21290043223527064, -0.3752419251539349, -0.9206095662278395, -1.2692337081427, -1.3069312998910974, -0.9856637364573758, -0.33589452924408947, 0.5378823464986151, 1.47769695327929, 2.30453434825355, 2.855833013883594, 3.020067979383654, 2.7609649641892773, 2.126035559618691, 1.237442580169654, 0.2669973405452208, -0.5994607069263358, -1.2007038479189613, -1.4334603507035257, -1.2732428657177821, -0.7781331985345223, -0.07471435180643912, 0.6707235381181027, 1.2892964033280865, 1.6466691892769576, 1.671898169197242, 1.3714808656876831, 0.8254546641756189, 0.16648035687279322, -0.45321681488379084, -0.8993042232222161, -1.088328545036719, -1.0082857970542387, -0.7216314567206173, -0.34966649358435486, -0.041672373684999424, 0.06406524093063468, -0.12198661165031646, -0.613449103955583, -1.3386662119900887, -2.152346960098917, -2.866515172220039, -3.2943382957357956, -3.296982901162272, -2.8223839355257847, -1.926107933045633, -0.7681496572952475, 0.41521735200966015, 1.3596640014619392, 1.831314844101818, 1.6828444440993873], 'positive_zeros': ['1.45390583995939883720046521228556', '3.02083321004080896155170308068728', '5.83677852176420868914421980282701', '7.28173288126409391739064551399770', '8.260960236549061719177728715996694', '9.188479679466817661547777377149761', '10.34315023876456713962016632620953', '11.69950957571609746995082346777426', '12.67448349900212106314621502601118', '13.75452316152219879934118989728789'], 'prelabel': '2-91-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.6253869637060793, 'root_number': '-0.3838062933361786 - 0.9234136284436911*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.312693481853', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45390583995939883720046521229', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02083321004080896155170308069', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.83677852176420868914421980283', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.10', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/q/a/36/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-91-13.10-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-91-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.31269348185303963, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45390583995939883720046521229', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1843044610699859971302967198590', 'Lhash_array': ['1843044610699859971302967198590'], 'label': '2-91-13.10-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/36/2'}